Phys. Rev. Lett. 57, 655–658 (1986)Fractal Dimension of CantoriReceived 2 May 1986; published in the issue dated 11 August 1986 At a critical point the golden-mean Kolmogrov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D=0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D=1 to the cantorus is governed by an exponent ν̅ =0.98… and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent. © 1986 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.57.655
DOI:
10.1103/PhysRevLett.57.655
PACS:
05.45.+b, 03.20.+i, 64.60.-i
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